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Functor vs Cofunctor - What's the difference?

functor | cofunctor |

As nouns the difference between functor and cofunctor

is that functor is (grammar) a function word while cofunctor is a contravariant functor.

functor

English

(wikipedia functor)

Noun

(en noun)
  • (grammar) a function word
  • (computing) a function object
  • (category theory) a structure-preserving mapping between categories: if F'' is a functor from category ''C'' to category ''D'', then ''F'' maps objects of ''C'' to objects of ''D'' and morphisms of ''C'' to morphisms of ''D'' such that any morphism ''f'':''X''→''Y'' of ''C'' is mapped to a morphism ''F''(''f''): ''F''(''X'') → ''F''(''Y'') of ''D , such that if h = g \circ f then F(h) = F(g) \circ F(f), and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

    • Hyponyms

    * (in category theory) endofunctor

    Derived terms

    * contravariant functor * representable functor ----

    cofunctor

    English

    Noun

    (en noun)
  • A contravariant functor.

    • External links

    * (wikipedia "cofunctor")